Bill Ackman's Pershing Square is betting that Chipotle Mexican Grill shares have already seen their worst days after a string of foodborne illnesses were linked to the restaurant, echoing comments Chipotle CFO John Hartung made in April.

"All the customer research points to the fact that we are recovering in the minds of our customers. In most cases we had bottomed in January, and we have been recovering steadily ever since," Hartung said in an interview on CNBC's "Mad Money."

He explained that the company's research revealed that "customers that visited Chipotle less often did not go to any other burrito joint. They didn't go to a direct competitor of Chipotle."

In a filing that disclosed a 9.9 percent stake in the company, Pershing said it intends to engage in discussions with the fast-casual restaurant company's board and management. It added the stock is undervalued and attractive.

Chipotle shares closed at $414.07 on Tuesday, a fraction of their 52-week high of $757. The stock has had a tough year and is down more than 13 percent.